The Bernoulli random variable is a discrete probability random variable with probability function given by:

subject to the following conditions:

The Bernoulli random variable comes about as a consequence of a single Bernoulli trial.  Success of the Bernoulli trial is indicated with x=1 and failure is indicated with x=0, where a success occurs with probability p.  The parameter p is also referred to as the Bernoulli probability parameter.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Statistics}\right]\right)\:$

$X≔\mathrm{BernoulliRandomVariable}\left(p\right)\:$

$\mathrm{ProbabilityFunction}\left(X\,0\right)$

$1-p$

$\mathrm{ProbabilityFunction}\left(X\,1\right)$

$p$

$\mathrm{Mean}\left(X\right)$

$p$

$\mathrm{Variance}\left(X\right)$

$p\left(1-p\right)$

$Y≔\mathrm{BernoulliRandomVariable}\left(\frac{1}{3}\right)\:$

$\mathrm{ProbabilityFunction}\left(Y\,x\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{CDF}\left(Y\,x\right)$

$\left\{\begin{array}{cc}0& x<0\\ \frac{2}{3}& x<1\\ 1& \mathrm{otherwise}\end{array}\right.$

$\mathrm{CDF}\left(Y\&comma;1\&comma;\mathrm{output}=\mathrm{plot}\right)$

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

Johnson, Norman L.; and Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

The Student[Statistics][BernoulliRandomVariable] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.